Our goal is to represent optimal transport maps on
Riemannian manifolds \(t:{\mathcal {M}}\rightarrow {\mathcal {M}}\) .
The key idea is to build upon the theory of
[1]} and parameterize the space of optimal
transport maps by \(c\) -concave functions \(\phi :{\mathcal {M}}\rightarrow {\mathcal {M}}\) , see
def:cconcave. Given a \(c\) -concave function, the map \(t\)  is
computed via e:ot. This requires computing the intrinsic
gradient of \(\phi \)  and the exponential map on \({\mathcal {M}}\) .
